Every Croteam fan who have played a bunch of any SS game have its own theories/assumptions about the game. You don't have to pay special attention to the whole universe of SS but I bet you have explained some parts of the game for yourself. Just because they seem too obvious for you or too absurd to be left unexplained. Here are mine assumptions about the lore:

Serious Sam is very good dancer. The gameplay of SS requires a lot of side stepping and going backwards. SS has served in the military but the thing that makes him special above the rest is that he is also the king of the dancefloor. That would explain why he is so successful at fighting monsters. We also have some multiplayer character with disco theme. And those characters are ingame because a)they are SS buddies b)they are good dancers = good at evading monsters.

Coop campaign happens after the solo campaign. I just love the idea that coop is basically fans/other time travelers trying to get to the Sam. They can do it because they are from different universe/time/they happen to found other time locks/the moon crashing the time lock + storm caused random people to be send back in time. They might have different intentions hence why we can have so many different characters in multiplayer. Some might just want to have Sam signature, some want to help him/be like him and some want to stop him or simply get something back from him (like stolen gun or even hearth c: ), or are here just by accident. But the thing that unites all those people/aliens/monsters is that they are not as good as SS so they need each other to defeat Mental's troops. That could be used as an explanation on why there is more monsters in coop (Mental just keep them spawning). I'd love this idea to be more developed: different looking locations in coop (other time of the day for example), more weapons etc. (BTW players with SS player models are just really good cosplayers ok? or his clones that time lock produced).

Sam has some special equipment that allows him to carry tons of weaponry. I honestly don't care what it is (shrinking device or portal like pocket) but it is there. The people in coop have it too because time lock copies it for some reason. That is all what I got here xd.

The beautiful thing is that everyone pays attention to different things. Because different people need different things to be explained to keep their suspension of disbelief. And that is why I encourage you to share your own theories.

At the end of TSE, Sam finally escaped Earth in the Sirian emergency vehicle, but it did NOT look like a NASA rocket as that would make no sense. Why would a race that uses giant flying saucers (which presumably use anti-gravity tech) use rockets? Can this rocket reach light speed? If not, Sam will be long dead before he ever reaches Sirius. So I retcon the story in my mind, and imagine he actually left in a more advanced Sirian craft.

Also, in "my" canon, the "SSS Centerprise" was taken down my Mental, not by the "crate bus".